This curiosity arises as follows: when ejecta from a strong solar flare hits Earth, will the Earth somehow counter its impact with a stronger magnetic field.
Or, earth's magnetic field as limited power strength to resist?
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$\begingroup$ I adjusted some of your wording to better fit the Stack Exchange style, but I think I've left the core of your question unchanged. It's a good question and in some cases impact of a high speed plasma can locally compress magnetic field lines, which could make the magnitude (strength) of the field stronger in that area, though the total flux from the Earth would remain essentially unchanged. Hopefully someone who is more knowledgable will write up a complete answer. $\endgroup$– uhohCommented Dec 17, 2019 at 10:24
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$\begingroup$ Solar flares do not, in general, affect Earth's magnetic field as they are intensifications of x-rays in a localized region on the Sun, e.g., see more at astronomy.stackexchange.com/a/16786/13663 $\endgroup$– honeste_vivereCommented Oct 14, 2022 at 13:24
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No, but the magnetic dipole of Earth has a field strength that increases with closer distance. On the direct line between Earth and Sun the magnetic field strength is always $B(r) = M/r^3$ where $M$ is the magnetic moment of the terrestrial dipole and $r$ is the distance to the dipole, aka Earth.
When the solar wind conditions change, the boundary between the wind and the terrestrial magnetosphere changes in location, until it finds a new pressure equilibrium.
The approximate location of the boundary shock can be found by equating the ram pressure of the solar win $p_{\rm ram}= \rho u^2$ with the magnetic dipole pressure $p_{\rm dip}=M^2/(2\mu_0 r^6)$, where $\mu_0$ is the vacuum magnetic permittivity. If you solve this for $r$, you will find a closer location $r$ for the shock for stronger conditions, and then checking at which magnetic field strength this occurs via $B(r) = M/r^3$, you'll find that the magnetic field at the shock has of course increased, but only because the shock has moved closer, not because $M$ has changed.
answered Dec 17, 2019 at 15:43